Is it permissible to make up for accumulated missed fasts over many years by fasting on Thursdays and Fridays of every week, knowing that the number of days is large and a long time has passed since they were missed, and is expiation obligatory in this case?

You are obligated to repent, seek forgiveness, and make up for all the Ramadan days you missed over the years, while also giving a mudd (a specific measure of food) to a poor person for each day due to delaying the make-up fasts beyond their due time. There is no harm in fasting on Thursday and Friday.

For every day you intended to fast, then broke your fast by intercourse during Ramadan, a major expiation (kaffarah kubra) is required of you. This is: freeing a slave; if you cannot find one, then fasting for two consecutive months; if you are unable to do that, then feeding sixty poor people. If your breaking of the fast was not by intercourse, but by eating or drinking, a group of scholars has held that expiation is also required in such cases.